Page 81 - Solutions Manual to accompany Electric Machinery Fundamentals

(a) The frequency of the voltage produced in this winding is

nP 1800 r/min 4 poles 
f  sm   60 Hz
se
120 120
(b) There are 24 slots on this stator, with 40 turns of wire per slot. Since this is a four-pole machine,
there are two sets of coils (in 8 slots) associated with each phase. The voltage in the coils in one pair of
slots is


E  A 2 N  C f  2  40 t 0.060 Wb 60 Hz   640 V
There are eight slots associated with each phase, and the all of the coils in a slot are connected in series,
so the total phase voltage is

 V   8 640 V  5120 V

Since the machine is Y-connected, V  L 3V   8868 V .

3-5. A three-phase Δ-connected six-pole winding is installed in 36 slots on a stator. There are 150 turns of
wire in each slot of the windings. All coils in each phase are connected in series. The flux per pole in the
machine is 0.060 Wb, and the speed of rotation of the magnetic field is 1000 r/min.
(a) What is the frequency of the voltage produced in this winding?
(b) What are the resulting phase and terminal voltages of this stator?

SOLUTION
(a) The frequency of the voltage produced in this winding is

nP 1000 r/min 6 poles 
f  sm   50 Hz
se
120 120
(b) There are 36 slots on this stator, with 150 turns of wire per slot. Since this is a six-pole machine,
there are three sets of coils (in 12 slots) associated with each phase. The voltage in the coils in one pair of
slots is
E  A 2 N  C f  2  150 t 0.060 Wb 50 Hz  2000 V

There are 12 slots associated with each phase, and the all of the coils in a slot are connected in series, so
the total phase voltage is
V   12 2000 V  24,000 V

Since the machine is Δ -connected, V  V  24,000 V .

L
3-6. A three-phase Y-connected 60-Hz two-pole synchronous machine has a stator with 5000 turns of wire per
phase. What rotor flux would be required to produce a terminal (line-to-line) voltage of 13.2 kV?
SOLUTION The phase voltage of this machine should be V   V L / 3  7621 V . The induced voltage per

phase in this machine (which is equal to V  at no-load conditions) is given by the equation


E  2 N 
f
A C
so
E 7621 V
  A   0.0057 Wb


2 Nf 2  5000 t 60 Hz 
C
75